Wing profile optimization method based on improved firefly algorithm

Abstract

The invention discloses a wing profile optimization method based on an improved firefly algorithm, belongs to the technical field of wing profile design, and solves the technical problems that multi-objective and nonlinear optimization conditions are difficult to process, the global optimization capability is insufficient and the design period is long in the traditional wing design process. The solution sequentially comprises the following steps of firefly algorithm improvement, airfoil data parameterization, parallel processing, constraint processing, external penalty function method, airfoil optimization, grid generation and flow field calculation. According to the method, the firefly algorithm is improved through the Matlab platform, the geometric shape of the airfoil is parameterized through the CST parameterization method, the lift-drag ratio of the airfoil serves as an optimization target, the airfoil is optimized through the improved firefly algorithm, the lift-drag ratio of the airfoil is improved, and then the aerodynamic performance of the airfoil is improved. The method has the advantages that the design is reasonable, the optimization precision is relatively high, and the designed wing section has high aerodynamic performance.

Description

Technical Field

[0001] The invention belongs to the technical field of airfoil design, relates to an aerodynamic shape design method, and specifically relates to a wing airfoil optimization method based on an improved firefly algorithm. Background Art

[0002] The wing is one of the important parts of an aircraft. It is installed on the fuselage and its main function is to generate lift. As a typical cross-section of an aircraft wing, the design of the airfoil determines the aerodynamic performance of the entire aircraft. At present, major aviation powers in the world have established their own airfoil series. The optimization design of aerodynamic shape is one of the key issues in aircraft design. Accurately predicting and optimizing the design of wing airfoils plays an important role in improving the flight performance of aircraft.

[0003] At present, traditional wing design methods are often designed based on engineering principles and empirical rules. During the design process, engineers usually need to manually adjust the parameters of the wing and airfoil, such as the twist angle, airfoil profile, etc., and most traditional methods are designed based on specific working conditions. They have limited ability to handle complex nonlinear problems and multi-aerodynamic target optimization problems. In addition, the design process requires a large number of experiments such as wind tunnel tests, repeated simulations and optimizations, which prolongs the R&D cycle and has high labor costs.

[0004] The firefly optimization algorithm simulates the social behaviors of fireflies such as foraging, courtship, and vigilance, which are displayed by the biological characteristics of luminescence, and searches for the optimal solution in the space. It can handle complex multi-objective optimization problems, adapt to different scenarios and problem types, and has good versatility. Therefore, it has important application value in wing airfoil optimization. However, the firefly algorithm is often prone to the dilemma of local optimal solutions during the optimization process, which is not enough to meet the requirements of the global optimization capability design of wing airfoils. Summary of the invention

[0005] The main purpose of the present invention is to overcome the deficiencies in the prior art and solve the technical problems that the traditional wing design process is difficult to handle multi-objective and nonlinear optimization situations, the global optimization capability is insufficient and the design cycle is long. The present invention provides a wing airfoil optimization method based on an improved firefly algorithm.

[0006] The design concept of the present invention is as follows: first, the firefly algorithm is improved, and then the improved firefly algorithm is used in combination with parallel processing and constraint processing to obtain the shape design variables of the wing airfoil; then, the wing airfoil is generated by the design variables using the CST parameterization method, and then a grid is generated from the wing airfoil, and the flow field and the aerodynamic parameters of the airfoil are calculated based on the grid; finally, the design target is determined by the aerodynamic parameters and the optimization is continued for multiple cycles to obtain a satisfactory airfoil.

[0007] In order to achieve the above-mentioned object of the invention, the present invention provides the following technical solutions:

[0008] A wing airfoil optimization method based on an improved firefly algorithm comprises the following steps:

[0009] S1. Improved Firefly Algorithm:

[0010] Since the firefly algorithm has a large number of local optimal solutions for many problems in actual engineering applications, there is a deviation from the ideal situation, which can easily cause the algorithm to fall into the local optimum, which may lead to the algorithm failing to converge. Therefore, the present invention introduces the population size d max , the firefly algorithm was improved by Matlab software, and the attraction formula was improved to:

[0011]

[0012] In formula (1), γ is the light absorption coefficient; β 0 Represents the attraction when the distance is "0"; r ij represents the Euclidean distance between firefly individuals i and j, k is the number of iterations, n is the maximum number of iterations; d max is the population size;

[0013] The present invention adopts the improved attraction formula. When two fireflies are far apart, they can still ensure the effective movement of the two fireflies, and can find the optimal solution in a larger range and move to it. max Finally, it is suitable for both large and small spaces;

[0014] S2. Airfoil data parameterization:

[0015] The CST parameterization method proposed and developed by Kulfan et al. is widely used in airfoil design research due to its good robustness, few parameters involved, high accuracy, simple and intuitive results, etc. CST parameterization uses shape function coefficients as design variables. When there are fewer design variables, it can accurately describe the geometric shape of the airfoil. The geometric shape of the airfoil is expressed by CST parameterization as follows:

[0016] y=C (x) ·S (x) +x·y (TE) ; (2)

[0017] Upper wing expression:

[0018] y 上 =C (x) ·S (x) +x·y (TE，上) ; (3)

[0019] The lower wing expression is:

[0020] y 下 =C (x) ·S (x) +x·y (TE，下) ; (4)

[0021] In equations (2) to (4), x and y represent dimensionless airfoil coordinates, and y (TE，上) ,y (TE，下) Represent the y coordinates of the trailing edges of the upper and lower wing surfaces respectively;

[0022] In formula (2) to formula (4), C (x) is a class function, expressed as:

[0023]

[0024] In formula (5), when N 1 、N 2 When the value of is different, y in formula (2) represents different geometric shapes;

[0025] In formula (2) to formula (4), S (x) is a shape function, which can further describe the geometric shape in detail and is expressed as follows using the n-order Bemstein polynomial:

[0026]

[0027] Then we have:

[0028]

[0029] In formula (7), A i A is the shape function coefficient (i.e., weighted coefficient), which can be changed according to different needs. i If the value of is used as the design variable of the optimization problem, the existing airfoil can be approximated by the least squares method. The objective function of solving the minimum value by the least squares method is:

[0030]

[0031] S3, parallel processing: using 4-core 4-thread Intel Xeon CPU E5-2650 processor, the main program controls 4 thread tasks respectively, the input value of each thread task is the same, and each task executes the optimization algorithm for airfoil optimization, grid generation, and flow field calculation. The 4 threads output 4 optimization results correspondingly, and the best result is selected as the final optimization result;

[0032] Parallel processing is a computing method that can perform two or more processes simultaneously in a computer system. Parallel processing can work on different levels of the same program at the same time, thus saving time in solving large and complex problems. In order to save the running time of the program, multiple targets are processed in the feasible area, which can greatly save the processing time for solving a series of complex problems and improve the efficiency of optimization;

[0033] S4. According to the characteristics of the constraints, the constraints are processed by the external penalty function method:

[0034] In engineering optimization, it is rare to encounter optimization solutions without constraints or linear constraints. Instead, single-objective optimization problems with complex constraints account for the vast majority, and some constraints are even extremely complex. However, adding constraints will reduce the search space of single-objective optimization, resulting in fewer available solutions. Therefore, the present invention converts the optimization problem with constraints into an unconstrained problem;

[0035] The penalty function is actually a constraint function, that is, a function that limits the constraint conditions. It is a solution to solve the optimal problem with constraints. It mainly converts a constrained optimal solution problem into a series of unconstrained problems. This series of unconstrained problems mainly consists of the original problem and the penalty function, plus the penalty factor. More importantly, the solution of this series of unconstrained problems will eventually converge to the solution of the original problem;

[0036] For nonlinear constraint programming:

[0037]

[0038] In formula (9), the constraint function P(x i , M) is the penalty function, M is the penalty factor, for the minimum value solution minf(x):

[0039]

[0040] Take a sufficiently large number M>0, the constructor is:

[0041]

[0042] Or the constructor is:

[0043]

[0044] In formula (12), M 1 、M 2 、M 3is a row vector, the augmented objective function P(x,M) is the unconstrained extreme value problem of the objective function, the optimal solution of minP(x,M) is also the optimal solution of the original problem, and the optimized airfoil geometry structure is obtained;

[0045] Through the improved firefly algorithm, the population size, iteration times and other parameters are set, the airfoil is optimized multiple times to obtain the best value, and the optimized airfoil is obtained;

[0046] S5. Meshing the airfoil geometry structure optimized in step S4 and performing flow field calculations. The Surro Opt program for solving two-dimensional flow fields is used to simulate and calculate the airfoil flow field:

[0047] Continuity equation:

[0048] Two-dimensional NS equations:

[0049] Transport equation of SA model: Where v is the molecular kinematic viscosity coefficient; G v is the turbulent viscosity derivative; and G b2 is a constant; Y v is the reduction term of the turbulent viscosity coefficient in the near-wall region; Customize source items for users;

[0050] This program uses the SA turbulence model to simulate turbulence, the Jameson center discretization format, and steady-state calculations;

[0051] Finally, the wing airfoil optimization design based on the improved firefly algorithm was completed.

[0052] Compared with the prior art, the present invention has the following beneficial effects:

[0053] 1. The present invention adopts an improved firefly algorithm to optimize the wing airfoil, which can fully consider multiple design objectives and constraints to obtain a better design result;

[0054] 2. The improved firefly algorithm has high search efficiency and global optimization capability, and can search for the optimal solution in a complex design space. By optimizing the design, the aerodynamic performance of the aircraft wing airfoil can be improved;

[0055] In conclusion, the present invention has reasonable design, high optimization accuracy, and is basically consistent with the actual results, thus avoiding the problem of local optimum and extending the application scope of the wing airfoil optimization method using the improved firefly algorithm. BRIEF DESCRIPTION OF THE DRAWINGS

[0056] Figure 1 It is a flowchart of the present invention;

[0057] Figure 2 The schematic diagram of the reference airfoil structure after parameterization by CST;

[0058] Figure 3 It is a schematic diagram of parallel computing process;

[0059] Figure 4 Schematic diagram of the external penalty function method;

[0060] Figure 5 This is a schematic diagram for comparing the front and rear airfoils for optimization;

[0061] Figure 6 Schematic diagram of pressure distribution curve for optimizing front and rear airfoils;

[0062] Figure 7 It is a schematic diagram of iterative convergence curve;

[0063] Figure 8 Grid division diagram;

[0064] Fig. 9 Local mesh division diagram of the leading edge;

[0065] Fig.10 Initial airfoil pressure cloud diagram;

[0066] Fig.11 Pressure cloud diagram of the airfoil after optimization. DETAILED DESCRIPTION

[0067] The present invention is further described in detail below in conjunction with the accompanying drawings and embodiments.

[0068] like Figure 1 The wing airfoil optimization method based on the improved firefly algorithm shown in the figure comprises the following steps:

[0069] S1. Improved Firefly Algorithm:

[0070] Introduced population size d max , the firefly algorithm was improved by Matlab software, and the attraction formula was improved to:

[0071]

[0072] In formula (1), γ is the light absorption coefficient; β 0 Represents the attraction when the distance is "0"; r ij represents the Euclidean distance between firefly individuals i and j, k is the number of iterations, n is the maximum number of iterations; d max is the population size;

[0073] The program source code of the improved firefly algorithm is as follows:

[0074]

[0075]

[0076] S2. Airfoil data parameterization:

[0077] In this specific implementation, RAE2822 is used as the reference airfoil, and the geometric shape of the airfoil is parameterized by CST as follows:

[0078] y=C (x) ·S (x) +x·y (TE) ; (2)

[0079] Upper wing expression:

[0080] y 上 =C (x) ·S (x) +x·y (TE，上) ; (3)

[0081] The lower wing expression is:

[0082] y 下 =C (x) ·S (x) +x·y (TE,下) ; (4)

[0083] In equations (2) to (4), x and y represent dimensionless airfoil coordinates, and y (TE，上) ,y (TE，下) Represent the y coordinates of the trailing edges of the upper and lower wing surfaces respectively;

[0084] In formula (2) to formula (4), C (x) is a class function, expressed as:

[0085]

[0086] In formula (5), when N 1 、N 2 When the value of is different, y in formula (2) represents different geometric shapes; in this specific implementation, N 1 =0.5, N 2 =1.0, indicating a round leading edge and a sharp trailing edge airfoil;

[0087] In formula (2) to formula (4), S (x) is the shape function, which is expressed by the n-order Bemstein polynomial:

[0088]

[0089] Then we have:

[0090]

[0091] In formula (7), A i is the shape function coefficient, and the objective function of solving the minimum value using the least squares method is:

[0092]

[0093] For the RAE2822 reference airfoil, 129 airfoil data points are used, and the parameterized airfoil is as follows: Figure 2 As shown;

[0094] S3, parallel processing: using 4 cores and 4 threads of Intel Xeon CPU E5-2650 processor, the main program controls 4 thread tasks respectively, the input value of each thread task is the same, and each task executes the optimization algorithm for airfoil optimization, grid generation, and flow field calculation. The 4 threads output 4 optimization results correspondingly, and the best result is selected as the final optimization result; the iterative code used in this specific implementation method selects quad-core parallel operation, and the parallel operation flow chart is as follows: Figure 3 As shown;

[0095] S4. According to the characteristics of the constraints, the constraints are processed by the external penalty function method. The penalty function strategy can be used to punish points that deviate from the feasible domain or deviate from the feasible domain, such as Figure 4 As shown:

[0096] For nonlinear constraint programming:

[0097]

[0098] In formula (9), the constraint function P(x i , M) is the penalty function, M is the penalty factor, for the minimum value solution minf(x):

[0099]

[0100] Take a sufficiently large number M>0, the constructor is:

[0101]

[0102] Or the constructor is:

[0103]

[0104] In formula (12), M 1 、M 2 、M 3is a row vector, the augmented objective function P(x,M) is the unconstrained extreme value problem of the objective function, the optimal solution of minP(x,M) is also the optimal solution of the original problem, and the optimized airfoil geometry structure is obtained;

[0105] The improved Firefly algorithm is used to optimize the RAE2822 airfoil multiple times to obtain the best value; the lift-to-drag ratio of the wing is used as the objective function; the calculation state: M a =0.75, R e =6.5×10 6 , α=2.31°, the population is selected as 24 fireflies, the number of iterations is selected as 50 times, and the comparison of the airfoil before and after optimization is shown in the figure below. Figure 5 As shown in Figure 1, it can be found that the front part of the upper surface of the optimized airfoil moves downward, the middle and rear parts move upward, and the transition is smoother. The pressure distribution curves of the airfoil before and after optimization are shown in Figure 1. Figure 6 As shown in , it can be found that the pressure distribution on the upper surface of the optimized airfoil is more stable and no longer has a large mutation. The iterative convergence curve is shown in Figure 7 As shown, it can be seen that better iteration results can be obtained by selecting a lower population size and number of iterations;

[0106] S5, meshing the airfoil geometry optimized in step S4. According to the optimized airfoil structure designed in this specific implementation method, the flow field is divided into a series of small grids. The size of the grid determines the calculation accuracy and computer processing time. Therefore, the grid division near the airfoil is denser, and the grid division far from the airfoil is sparser. In this way, the calculation time can be reduced while ensuring the calculation accuracy. Figure 8 , Fig. 9 As shown. On this basis, the flow field calculation is carried out, and the Surro Opt (2013RS029774) program for solving two-dimensional flow fields is used to simulate and calculate the airfoil flow field:

[0107] Continuity equation:

[0108] Two-dimensional NS equations:

[0109] Transport equation of SA model:

[0110] Complete the wing airfoil optimization design based on the improved firefly algorithm.

[0111] In this specific implementation manner, the cloud chart format in Tecplot uses the settings of Modified Rainbow-Less Green, Minimum-level: 0.515, Maximum-level: 1.425, Number of levels: 400 to draw a comparison of the pressure cloud charts of the reference airfoil and the optimized airfoil, as shown in FIG. Fig.10 , Fig.11 As shown, it can be seen that the shock wave intensity of the optimized airfoil is weakened when Ma=0.75.

[0112] The above is only a specific embodiment of the present invention, but the protection scope of the present invention is not limited thereto. Any changes or substitutions that can be easily thought of by a person skilled in the art within the technical scope disclosed by the present invention should be included in the protection scope of the present invention. Therefore, the protection scope of the present invention shall be based on the protection scope of the claims.

Claims

1. A wing airfoil optimization method based on an improved firefly algorithm, characterized in that: The following steps are involved: S1. Improved Firefly Algorithm: Introduced population size d max , the firefly algorithm was improved by Matlab software, and the attraction formula was improved to: In formula (1), y is the light absorption coefficient; β0 represents the attraction when the distance is "0"; r ij represents the Euclidean distance between firefly individuals i and j, k is the number of iterations, n is the maximum number of iterations; d max is the population size; S2. Airfoil data parameterization: The airfoil geometry is parameterized using CST as follows: y=C (x) ·S (x) +x·y (TE) ; (2) Upper wing expression: y 上 =C (x) ·S (x) +x·y (TE，上) ; (3) Lower wing expression: y 下 =C (x) ·S (x) +x·y (TE，下) ; (4) In equations (2) to (4), x and y represent dimensionless airfoil coordinates, and y (TE，上) ,y (TE，下) Represent the y coordinates of the trailing edges of the upper and lower wing surfaces respectively; In formula (2) to formula (4), C (x) is a class function, expressed as: In formula (5), when the values ​​of N1 and N2 are different, y in formula (2) represents different geometric shapes; In formula (2) to formula (4), S (x) is the shape function, which is expressed by the n-order Bemstein polynomial: Then we have: In formula (7), A i is the shape function coefficient, and the objective function for solving the minimum value using the least squares method is: S3, parallel processing: using 4-core 4-thread Intel Xeon CPU E5-2650 processor, the main program controls 4 thread tasks respectively, the input value of each thread task is the same, and each task executes the optimization algorithm for airfoil optimization, grid generation, and flow field calculation. The 4 threads output 4 optimization results correspondingly, and the best result is selected as the final optimization result; S4. According to the characteristics of the constraints, the constraints are processed by the external penalty function method: For nonlinear constraint programming: In formula (9), the constraint function P(x i , M) is the penalty function, M is the penalty factor, for the minimum value solution min f(x): Take a sufficiently large number M>0, the constructor is: Or the constructor is: P(x,M)=f(x)+M1max(G(x),0)-M2min(H(x),0)+M3|K(x)|; (12) In formula (12), M1, M2, M3 are row vectors; Obtaining an optimized airfoil geometry; S5. Meshing the airfoil geometry structure optimized in step S4 and performing flow field calculations. The Surro Opt program for solving two-dimensional flow fields is used to simulate and calculate the airfoil flow field: Continuity equation: Two-dimensional NS equations: Transport equation of SA model: Complete the wing airfoil optimization design based on the improved firefly algorithm.

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